Question

Assume ABC Corp. pays the dividend of $4.55 this year. For the next 30 years, the firm's dividend will grow by 5.4%, then will grow by 4.7% each year afterwards. The required rate of return for the firm's industry is 10.8%. What is the present value of the firm's stock under the Dividend Discount Model?

Answer 1

$86.42

Step-by-step explanation:

Div₀ = $4.55

using an excel spreadsheet I determined the next 29 dividends:

Div₁ = $4.80

Div₂ = $5.05

Div₃ = $5.33

Div₄ = $5.62

Div₅ = $5.92

Div₆ = $6.24

Div₇ = $6.57

Div₈ = $6.93

Div₉ = $7.30

Div₁₀ = $7.70

Div₁₁ = $8.11

Div₁₂ = $8.55

Div₁₃ = $9.01

Div₁₄ = $9.50

Div₁₅ = $10.01

Div₁₆ = $10.56

Div₁₇ = $11.13

Div₁₈ = $11.73

Div₁₉ = $12.36

Div₂₀ = $13.03

Div₂₁ = $13.73

Div₂₂ = $14.47

Div₂₃ = $15.25

Div₂₄ = $16.08

Div₂₅ = $16.94

Div₂₆ = $17.86

Div₂₇ = $18.82

Div₂₈ = $19.84

Div₂₉ = $20.91

Div₃₀ = $4.55 x (1 + 5.4%)³⁰ = $22.0409

Div₃₁ = $22.0409 x 1.047 = $23.08

first we must determine the terminal value at year 30 = $23.08 / (10.8% - 4.7%) = $378.36

again I used an excel spreadsheet to discount the 30 future dividends using a 10.8% discount rate = $68.97 + $378.36/1.108³⁰ = $86.42